\(\int \frac {(96 x^2-3 x^3+e^x (-32 x^3+x^4)) \log (e^{-x} (-3+e^x x))+(-1728 x+54 x^2+e^x (-576 x+18 x^2)+(54 x-18 e^x x^2) \log (e^{-x} (-3+e^x x))) \log (-\frac {16 \log (e^{-x} (-3+e^x x))}{-32+x})+(-864+27 x+e^x (288 x-9 x^2)) \log (e^{-x} (-3+e^x x)) \log ^2(-\frac {16 \log (e^{-x} (-3+e^x x))}{-32+x})}{(96 x^2-3 x^3+e^x (-32 x^3+x^4)) \log (e^{-x} (-3+e^x x))} \, dx\) [1798]

Optimal result

Integrand size = 212, antiderivative size = 30 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=x+\frac {9 \log ^2\left (\frac {\log \left (-3 e^{-x}+x\right )}{2-\frac {x}{16}}\right )}{x} \] Output:

x+9*ln(ln(x-3/exp(x))/(2-1/16*x))^2/x
 

Mathematica [F]

\[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx \] Input:

Integrate[((96*x^2 - 3*x^3 + E^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x] + 
(-1728*x + 54*x^2 + E^x*(-576*x + 18*x^2) + (54*x - 18*E^x*x^2)*Log[(-3 + 
E^x*x)/E^x])*Log[(-16*Log[(-3 + E^x*x)/E^x])/(-32 + x)] + (-864 + 27*x + E 
^x*(288*x - 9*x^2))*Log[(-3 + E^x*x)/E^x]*Log[(-16*Log[(-3 + E^x*x)/E^x])/ 
(-32 + x)]^2)/((96*x^2 - 3*x^3 + E^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x 
]),x]
 

Output:

Integrate[((96*x^2 - 3*x^3 + E^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x] + 
(-1728*x + 54*x^2 + E^x*(-576*x + 18*x^2) + (54*x - 18*E^x*x^2)*Log[(-3 + 
E^x*x)/E^x])*Log[(-16*Log[(-3 + E^x*x)/E^x])/(-32 + x)] + (-864 + 27*x + E 
^x*(288*x - 9*x^2))*Log[(-3 + E^x*x)/E^x]*Log[(-16*Log[(-3 + E^x*x)/E^x])/ 
(-32 + x)]^2)/((96*x^2 - 3*x^3 + E^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x 
]), x]
 

Rubi [F]

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

\(\displaystyle \int \frac {\left (e^x \left (288 x-9 x^2\right )+27 x-864\right ) \log \left (e^{-x} \left (e^x x-3\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (e^x x-3\right )\right )}{x-32}\right )+\left (54 x^2+e^x \left (18 x^2-576 x\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (e^x x-3\right )\right )-1728 x\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (e^x x-3\right )\right )}{x-32}\right )+\left (-3 x^3+96 x^2+e^x \left (x^4-32 x^3\right )\right ) \log \left (e^{-x} \left (e^x x-3\right )\right )}{\left (-3 x^3+96 x^2+e^x \left (x^4-32 x^3\right )\right ) \log \left (e^{-x} \left (e^x x-3\right )\right )} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (-\frac {9 \log ^2\left (-\frac {16 \log \left (x-3 e^{-x}\right )}{x-32}\right )}{x^2}-\frac {18 \left (\left (e^x x-3\right ) \log \left (x-3 e^{-x}\right )-\left (e^x+3\right ) (x-32)\right ) \log \left (-\frac {16 \log \left (x-3 e^{-x}\right )}{x-32}\right )}{(x-32) x \left (e^x x-3\right ) \log \left (x-3 e^{-x}\right )}+1\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -9 \int \frac {\log ^2\left (-\frac {16 \log \left (x-3 e^{-x}\right )}{x-32}\right )}{x^2}dx+18 \int \frac {\log \left (-\frac {16 \log \left (x-3 e^{-x}\right )}{x-32}\right )}{x^2 \log \left (x-3 e^{-x}\right )}dx+54 \int \frac {\log \left (-\frac {16 \log \left (x-3 e^{-x}\right )}{x-32}\right )}{x^2 \left (e^x x-3\right ) \log \left (x-3 e^{-x}\right )}dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (x-3 e^{-x}\right )}{x-32}\right )}{x-32}dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (x-3 e^{-x}\right )}{x-32}\right )}{x}dx+54 \int \frac {\log \left (-\frac {16 \log \left (x-3 e^{-x}\right )}{x-32}\right )}{x \left (e^x x-3\right ) \log \left (x-3 e^{-x}\right )}dx+x\)

Input:

Int[((96*x^2 - 3*x^3 + E^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x] + (-1728 
*x + 54*x^2 + E^x*(-576*x + 18*x^2) + (54*x - 18*E^x*x^2)*Log[(-3 + E^x*x) 
/E^x])*Log[(-16*Log[(-3 + E^x*x)/E^x])/(-32 + x)] + (-864 + 27*x + E^x*(28 
8*x - 9*x^2))*Log[(-3 + E^x*x)/E^x]*Log[(-16*Log[(-3 + E^x*x)/E^x])/(-32 + 
 x)]^2)/((96*x^2 - 3*x^3 + E^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x]),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 16.62 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30

method	result	size
parallelrisch	\(\frac {384 x^{2}+3456 {\ln \left (-\frac {16 \ln \left (\left ({\mathrm e}^{x} x -3\right ) {\mathrm e}^{-x}\right )}{x -32}\right )}^{2}+6144 x}{384 x}\)	\(39\)

Input:

int((((-9*x^2+288*x)*exp(x)+27*x-864)*ln((exp(x)*x-3)/exp(x))*ln(-16*ln((e 
xp(x)*x-3)/exp(x))/(x-32))^2+((-18*exp(x)*x^2+54*x)*ln((exp(x)*x-3)/exp(x) 
)+(18*x^2-576*x)*exp(x)+54*x^2-1728*x)*ln(-16*ln((exp(x)*x-3)/exp(x))/(x-3 
2))+((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)*ln((exp(x)*x-3)/exp(x)))/((x^4-32*x 
^3)*exp(x)-3*x^3+96*x^2)/ln((exp(x)*x-3)/exp(x)),x,method=_RETURNVERBOSE)
 

Output:

1/384*(384*x^2+3456*ln(-16*ln((exp(x)*x-3)/exp(x))/(x-32))^2+6144*x)/x
 

Fricas [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\frac {x^{2} + 9 \, \log \left (-\frac {16 \, \log \left ({\left (x e^{x} - 3\right )} e^{\left (-x\right )}\right )}{x - 32}\right )^{2}}{x} \] Input:

integrate((((-9*x^2+288*x)*exp(x)+27*x-864)*log((exp(x)*x-3)/exp(x))*log(- 
16*log((exp(x)*x-3)/exp(x))/(x-32))^2+((-18*exp(x)*x^2+54*x)*log((exp(x)*x 
-3)/exp(x))+(18*x^2-576*x)*exp(x)+54*x^2-1728*x)*log(-16*log((exp(x)*x-3)/ 
exp(x))/(x-32))+((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)*log((exp(x)*x-3)/exp(x) 
))/((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)/log((exp(x)*x-3)/exp(x)),x, algorith 
m="fricas")
 

Output:

(x^2 + 9*log(-16*log((x*e^x - 3)*e^(-x))/(x - 32))^2)/x
 

Sympy [A] (verification not implemented)

Time = 0.89 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=x + \frac {9 \log {\left (- \frac {16 \log {\left (\left (x e^{x} - 3\right ) e^{- x} \right )}}{x - 32} \right )}^{2}}{x} \] Input:

integrate((((-9*x**2+288*x)*exp(x)+27*x-864)*ln((exp(x)*x-3)/exp(x))*ln(-1 
6*ln((exp(x)*x-3)/exp(x))/(x-32))**2+((-18*exp(x)*x**2+54*x)*ln((exp(x)*x- 
3)/exp(x))+(18*x**2-576*x)*exp(x)+54*x**2-1728*x)*ln(-16*ln((exp(x)*x-3)/e 
xp(x))/(x-32))+((x**4-32*x**3)*exp(x)-3*x**3+96*x**2)*ln((exp(x)*x-3)/exp( 
x)))/((x**4-32*x**3)*exp(x)-3*x**3+96*x**2)/ln((exp(x)*x-3)/exp(x)),x)
 

Output:

x + 9*log(-16*log((x*exp(x) - 3)*exp(-x))/(x - 32))**2/x
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (26) = 52\).

Time = 0.21 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.37 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\frac {x^{2} + 144 \, \log \left (2\right )^{2} + 18 \, {\left (4 \, \log \left (2\right ) - \log \left (x - 32\right )\right )} \log \left (x - \log \left (x e^{x} - 3\right )\right ) + 9 \, \log \left (x - \log \left (x e^{x} - 3\right )\right )^{2} - 72 \, \log \left (2\right ) \log \left (x - 32\right ) + 9 \, \log \left (x - 32\right )^{2}}{x} \] Input:

integrate((((-9*x^2+288*x)*exp(x)+27*x-864)*log((exp(x)*x-3)/exp(x))*log(- 
16*log((exp(x)*x-3)/exp(x))/(x-32))^2+((-18*exp(x)*x^2+54*x)*log((exp(x)*x 
-3)/exp(x))+(18*x^2-576*x)*exp(x)+54*x^2-1728*x)*log(-16*log((exp(x)*x-3)/ 
exp(x))/(x-32))+((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)*log((exp(x)*x-3)/exp(x) 
))/((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)/log((exp(x)*x-3)/exp(x)),x, algorith 
m="maxima")
 

Output:

(x^2 + 144*log(2)^2 + 18*(4*log(2) - log(x - 32))*log(x - log(x*e^x - 3)) 
+ 9*log(x - log(x*e^x - 3))^2 - 72*log(2)*log(x - 32) + 9*log(x - 32)^2)/x
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 426 vs. \(2 (26) = 52\).

Time = 3.60 (sec) , antiderivative size = 426, normalized size of antiderivative = 14.20 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx =\text {Too large to display} \] Input:

integrate((((-9*x^2+288*x)*exp(x)+27*x-864)*log((exp(x)*x-3)/exp(x))*log(- 
16*log((exp(x)*x-3)/exp(x))/(x-32))^2+((-18*exp(x)*x^2+54*x)*log((exp(x)*x 
-3)/exp(x))+(18*x^2-576*x)*exp(x)+54*x^2-1728*x)*log(-16*log((exp(x)*x-3)/ 
exp(x))/(x-32))+((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)*log((exp(x)*x-3)/exp(x) 
))/((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)/log((exp(x)*x-3)/exp(x)),x, algorith 
m="giac")
 

Output:

-1/2*(9*pi^2*sgn(-8*pi + 8*pi*sgn(x*e^x - 3))*sgn(x - 32)*sgn(log(abs(x*e^ 
x - 3)*e^(-x))) + 9*pi^2*sgn(-8*pi + 8*pi*sgn(x*e^x - 3))*sgn(x - 32) + 27 
*pi^2*sgn(-8*pi + 8*pi*sgn(x*e^x - 3))*sgn(log(abs(x*e^x - 3)*e^(-x))) - 1 
8*pi*arctan(-1/2*(pi - pi*sgn(x*e^x - 3))/log(abs(x*e^x - 3)*e^(-x)))*sgn( 
-8*pi + 8*pi*sgn(x*e^x - 3))*sgn(log(abs(x*e^x - 3)*e^(-x))) + 27*pi^2*sgn 
(-8*pi + 8*pi*sgn(x*e^x - 3)) - 18*pi*arctan(-1/2*(pi - pi*sgn(x*e^x - 3)) 
/log(abs(x*e^x - 3)*e^(-x)))*sgn(-8*pi + 8*pi*sgn(x*e^x - 3)) + 27*pi^2*sg 
n(x - 32) - 18*pi*arctan(-1/2*(pi - pi*sgn(x*e^x - 3))/log(abs(x*e^x - 3)* 
e^(-x)))*sgn(x - 32) + 9*pi^2*sgn(log(abs(x*e^x - 3)*e^(-x))) + 54*pi^2 - 
2*x^2 - 54*pi*arctan(-1/2*(pi - pi*sgn(x*e^x - 3))/log(abs(x*e^x - 3)*e^(- 
x))) + 18*arctan(-1/2*(pi - pi*sgn(x*e^x - 3))/log(abs(x*e^x - 3)*e^(-x))) 
^2 - 18*log(16*abs(log((x*e^x - 3)*e^(-x))))^2 + 36*log(16*abs(log((x*e^x 
- 3)*e^(-x))))*log(abs(x - 32)) - 18*log(abs(x - 32))^2)/x
 

Mupad [B] (verification not implemented)

Time = 2.04 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=x+\frac {9\,{\ln \left (-\frac {16\,\ln \left (x-3\,{\mathrm {e}}^{-x}\right )}{x-32}\right )}^2}{x} \] Input:

int((log(exp(-x)*(x*exp(x) - 3))*(exp(x)*(32*x^3 - x^4) - 96*x^2 + 3*x^3) 
+ log(-(16*log(exp(-x)*(x*exp(x) - 3)))/(x - 32))*(1728*x + exp(x)*(576*x 
- 18*x^2) - log(exp(-x)*(x*exp(x) - 3))*(54*x - 18*x^2*exp(x)) - 54*x^2) - 
 log(exp(-x)*(x*exp(x) - 3))*log(-(16*log(exp(-x)*(x*exp(x) - 3)))/(x - 32 
))^2*(27*x + exp(x)*(288*x - 9*x^2) - 864))/(log(exp(-x)*(x*exp(x) - 3))*( 
exp(x)*(32*x^3 - x^4) - 96*x^2 + 3*x^3)),x)
 

Output:

x + (9*log(-(16*log(x - 3*exp(-x)))/(x - 32))^2)/x
 

Reduce [B] (verification not implemented)

Time = 0.21 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.13 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\frac {9 {\mathrm {log}\left (-\frac {16 \,\mathrm {log}\left (\frac {e^{x} x -3}{e^{x}}\right )}{x -32}\right )}^{2}+x^{2}}{x} \] Input:

int((((-9*x^2+288*x)*exp(x)+27*x-864)*log((exp(x)*x-3)/exp(x))*log(-16*log 
((exp(x)*x-3)/exp(x))/(x-32))^2+((-18*exp(x)*x^2+54*x)*log((exp(x)*x-3)/ex 
p(x))+(18*x^2-576*x)*exp(x)+54*x^2-1728*x)*log(-16*log((exp(x)*x-3)/exp(x) 
)/(x-32))+((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)*log((exp(x)*x-3)/exp(x)))/((x 
^4-32*x^3)*exp(x)-3*x^3+96*x^2)/log((exp(x)*x-3)/exp(x)),x)
 

Output:

(9*log(( - 16*log((e**x*x - 3)/e**x))/(x - 32))**2 + x**2)/x